{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# 邻接矩阵$A$的幂\n",
    "\n",
    "$$\n",
    "\n",
    "f(A)=I+A+A^2+\\cdots+\n",
    "\n",
    "$$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import seaborn as sns\n",
    "import matplotlib.pyplot as plt\n",
    "from pathlib import Path as P\n",
    "import scipy.io as sio\n",
    "import numpy as np\n",
    "import scipy.sparse as sp\n",
    "from dataclasses import dataclass\n",
    "from sklearn.metrics.pairwise import pairwise_distances"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "dict_keys(['__header__', '__version__', '__globals__', 'X1', 'X2', 'X_names', 'Y'])"
      ]
     },
     "execution_count": 2,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "data=sio.loadmat(r'Output\\cite-content\\Cornell.mat',simplify_cells=True)\n",
    "# [x.shape for x in data['X']]\n",
    "data.keys()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(195, 195)"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "X1=data['X1']\n",
    "X1.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(0.5, 1.0, 'X1')"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "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",
      "text/plain": [
       "<Figure size 432x288 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "sns.heatmap(X1)\n",
    "plt.title('X1')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [],
   "source": [
    "X2 = X1 + X1@X1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(0.5, 1.0, 'X2')"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAWMAAAERCAYAAACuKMYrAAAAOXRFWHRTb2Z0d2FyZQBNYXRwbG90bGliIHZlcnNpb24zLjQuMywgaHR0cHM6Ly9tYXRwbG90bGliLm9yZy/MnkTPAAAACXBIWXMAAAsTAAALEwEAmpwYAABLtUlEQVR4nO29eZwuRXno/33mnZkzcxYO5xyQ3RxUkKhRNIgYY0RxweWKMcZAjFswJLkuaEwi3uT+1NzkBr1GYz6J/kJcwERBVIxolEUEuflFdpDtsMl+2BEOh7POzPv8/ujuOTU1vVR3V/fb7zv1nU9/5u3u6qqnqqurq596nipRVQKBQCAwWMYGLUAgEAgEQmMcCAQCnSA0xoFAINABQmMcCAQCHSA0xoFAINABQmMcCAQCHSA0xoFAINABQmMcGCgislJE7hSRtxnHVonI3SLyFhH5MxG5XkQ2i8gdIvJng5Q3EGiK0BgHBoqqPgn8IfD3IrJnfPhTwBWq+i1AgHcAa4CjgfeJyLEDETYQaBAJHniBLiAipwLLgH8Gvg08W1UfSAn3D0T19v3tShgINEvoGQe6woeAI4FvAX+a0RAL8FLghnZFCwSaJzTGgU6gqo8RNbLLgbMygn2cqM5+pSWxAoHWCI1xoBOIyO8B64EfAZ9MOf8+It3x61V1R7vSBQLNE3TGgYEjIk8h6hW/Fbgp/n2Mqv7f+PzvA38F/Iaq3j4wQQOBBgmNcWDgiMiZwCZV/YN4/z3AnwLPA94C/B3wclXdMDgpA4FmCY1xYKCIyJuAzwPPUtXHjeM/Bn4K/C6wP2CqJv5NVf+oRTEDgcYJjXEgEAh0gDCAFwgEAh2gscZYRI4WkZtF5DYROampdAKBQGAUaERNISI94BbgVcC9wOXAcap6o/fEAoFAYARoqmd8OHCbqt6uqjuBM4BjGkorEAgEhp7xhuLdD7jH2L8XeFFW4D1XP1MBHtv2ZEPiFDPRi4piZm52YDIMgoneeOfzvGpyGoDNO7flhls+sYytM8EfBGBMhL6Hr15f8RRRph7O7twoddObeeR250xN7PG02um50FRjXIiInACcACC91YyNrWDP5at5dNsTC27+mOwqh77q/H5flTXTK9m0fcv8vhneDFu031dlrj+3KD0zXJpMdpwu2HLmyWeSlxeA3lgPYD4f9n5aun1VZuZmc/NjXpcnU5rMZTBlsEka4SIZts/uXHDcVyNiprFiYir1pZAnf5n40+px0TV2uCTvafe1TD3LO+Yib9F1Zgdorj+XKWNvrLeoHtcmjq9LNNUYbwQOMPb3j4/No6qnAKcAjE/upwCPbnuiVCJJQxzY1aNPKvFcBytbHm30vnxQ1DsPuONaR80Ogze07zc+DzTVGF8OHCQiBxI1wscSGe8HAoHA4OkvkcZYVWfjiV3OBXrAl1W1cNrDtE8eu8dk7qf1pvLOl42r7nV5pH0eVpUhTYWRFVfZMsv7XG6yN5uWbpEMeZ/fdXCJq056Zcq2jDokq+zK1DNXqtSPqs+qD7SD4ySN6YxV9QfAD6pcm6enHFVsvV7Za/P268pVlyr3sUq6S6GuNP1iWDIsITVFJezGqGjQrWjgo8wAXpZOqs0BPDP+sgN4WfHmnS8qMztM1QE8nwNprjI0NYDno8fqEn+XBvDyqDOAV/VZ9UIHx1Q61RhnsWJiCoAtM9vnjxVVmjoK/8QSAci9aWMiC0Z662JbQGQx0RvPDDM1PrnAqsAXvbEe9OcWPHw+894WWSaMTXyFVYmziXrtck3V58X7wFpbjFrPWES+DLwBeEhVnxMfWwt8g2ii8DuBt8arOBSSpXdKGuGp8cl5O9Ksiu5D99s3Rm/NNLPCViFNzjw7SzN8L+N6gBmjwXRNt4o+sTfWa90+ucz9zjo+Eb/wbJO+tPtcFFdV2aqGKytL8t+24W1L/99lnXEXB/DqeuCdSrRir8lJwAWqehBwQbzvJozIojetub91ZgdrpleyZnrl/KeLfY25b5/P2rfP2WkmvSmIKnbedUWbLWeefGllMyYy35CkhU/sNV3STfJlyzDRG5/Ppy1Dci5PhqYoKhc7n2nXbp3ZMd/o9nXXAPHWmR2ZeXHJo2sZmGHs8s+qx3np5T0zafWlKD9167NrXPY1WefS6qgPVPvOW1vUnptCRNYD3zd6xjcDR6rq/SKyD3CRqj4zL47EzjgL8ya0NbiXlmZXyMt7U+Vix9t0+TdFm2qKrjBqefPhgbfjlv90LpBlB//60Hrg7aWq98e/HwD2cr0w8ajLM1dK9vvq1wMv663b5gBe3gsgLy+wUN+cJlPdAby0+FzD+iKtUcmSIasBylKt5MluprEUPfDyaGMAL3jgeUBVVURSSy/NHToQCARaYdQG8DJ4UET2MdQUD6UFSnOHLuveHNyhd2G7QweaIbhDt08j7tAdHMBrojE+G3gncHL8/7uuF7qM8maNwCafZlVHaPP0oa7XlcGnJYhrHC7plom3bT1kkQxN6fnTPuVd7oerrrZK2brUlUxroZLWNi7UzUPr1hSj1jMWkdOBI4E9RORe4GNEjfCZInI8cBfR8uuNk6bbrRPXqJCnZx1kPpuQwXd+smRswmStrAyBmoxaz1hVj8s4dVSV+IoGAYqU/n1VXrznIQD89OGbvA7gJY4nm3dua2QALytcQtEAXl68ZoOcdd4l3jyZ8ux0IZqTeGp8Mgrbm+CezY/Mnztw9d7csemBzGvT8pEmQ5G8Zcka9Eybezer0XTprZcZwMurp2aYrg/gPX31vvx8032ZMuU9qz7Q/oyXeHzSidWhXU3bytyIOpOmu147JjIQ54dBmLb5SGtUenmu+R41k7I0BnFPfZi2bb/qbGeBp17wxqE1bauMy9u16A2fHLOV/mV6xmkTXafJ1FeFDFOyLLJ6qGV6LHk92LS4s9JN69WU7WmW0dPWfWDb7hmnpWGPS9hhqownBNO2AcxN0UGdcWUPPBE5QEQuFJEbReQGETkxPr5WRM4XkVvj/2v8iRsIBAIe6M+5by1Rp2c8C3xYVa8SkVXAlSJyPvAuInfok0XkJCJ36I+4ROgyIlvU88g6n7Y+WpUR5iJLC1eKZLf1vEU9Gld5zHhcLFDs42YPpe1PcJcyywvrM12TMr3wNBld6n2Z82nxVqnrZXCpj3bvNk+mov3adLBnXLkxjr3s7o9/bxaRDUQLkR5DZGEBcBpwEY6Ncd0BPDsO83wy94BLXCa2msL1uiyqqCnS0ikzgJd1voqaIu8ztOnG2UVNkRe2TroJWQ2n62e0q6pnFNQUWfHlyVe0762Ojerk8vH8FM8HLqWGO3QgEAi0QgdN2+rO2oaIrAS+DXxQVResKKqRqUbqq0xEThCRK0Tkin6/XU+6ddO7tZoeRHMaJOZxgWYoKl9z9r2AXxKzxaGh33ffWqKu08cEUUP8NVU9Kz5c2R26SZ2xuf/w1k1Oc7xWlSFtZjDbjbasntBVh1blM7mMzrhMWr4pkmH73Exu2KomiC75rFMWw6YzTqvfaTbmZfLQts5YdYQmChIRAb4EbFDVzxinKrtDN6kztvdn5mYXVCpXnXFeGgnJDFOuJmZ5+bHTzEq3LZ1xlkxpMvumSAZz1ZEinXHdQbesMFXKYNh0xmb9zpO3CdM2b3RQTVGnZ/wS4O3AdSJyTXzsf1DDHbqtnnFC8mYvcvJwlaHMA952zzjv4R6VnnGZB7bMfQs942Lq5qHtnvGoWVP8J5BV+0u5Qyc91LQ5S5vqGZv7M3OzrJleCSyeCa5sz7ioQehaz3jV5PT8slbD3jMucsnOokjuYewZ23MAV+0ZF62p2HbP2FsdG1Vrirp0YfrHpTodpznXxrDTxEKsw4qvaSdHtkw7qKaobU3RBr2x3sIVm1OwK16dkXNXq4cxkYGMIuc9ZEXl5JOyaY1JO2vlNY1rHkYhr0UM7T3VvvvWEnXcoadE5DIR+VnsDv2J+PiBInKpiNwmIt8QEW+tlXnTiz6R60zes2Vm+/wLoOhTa2R7DhZ2wzsmsmDAzIW+tu+1Z5MsqGpTVd/sI1zTNNlYduGeVsKjaZuIfChuA68XkdPjtrF0O1inZ7wDeIWqPg84FDhaRI4APgl8VlWfATwGHO8aYdqN7asy159jrj/H1PjkgjDJb3sgIOt81r59zkxzxcRUqkxZ1xVtdhxF+UkL3xvrZcY7kXIuK12X/GSRJ0NTFJWLyyDVxFiPifjFYvbq8r5w0uK3e4R1yqDonhRdk1Y/zTDmvcpKLyvesvXZNS77mjLPqhc8NcYish/wAeCweFHmHnAsFdrByo2xRjwZ707EmwKvAL4VHz8NeFPVNAKBQKAR/KopxoFpERkHlhNNE1G6Hazr9NEDrgSeAfwT8HPgcVVNdAT3Es1X4UTRiOzWmR2ZtsHJNVVHaLM+5Tbv3Maqyel5p42J3njqKLUrtpx58pnYNtJZaprtszud7ZuTuZiLVDEmebbZTfeOi6wpzLmls8zVTGsL87w5d0leGmZPLS1MmTKw7YFt+fPiK2NnbN6rMvXMhbTnziWuvOcvrUwGaU1hLp4cc0rstIaqbhSRTwN3A9uA84jaxNLtYN2VPuaAQ0Vkd+A7wCGu16atDp312WRS5DVnrsiR9fmWtp93kzfv3JbqdVR0XR4uec07lxW2SJ4FeY7z4pKHJN+uXos2ibmVHR+4T+ZfVGb9irIVXeMSV5305v+XkN+lrmTV7zL1zJWy9dns4KSFtcvE+4u+hDWF6S1sE08RfAxwIPA48E3g6CoiebGmUNXHgQuBFwO7x911gP2BjRnXnKKqh6nqYWNjK5zTyhqASdi8c1vqCr51BjGSxmJmbpYDVu1ROZ4ypMnre+R61eR0appp6STHVk1Os2pyulIPKilDu+H1tVJKXr1wkXf5xDKWTyxrdMBr+cSy+d92+Q+Stq0iXFfZbkwmf2qKVwJ3qOrDqjoDnEXkEOfUDprUcYfeE5hR1cdFZBp4FZHS+kLgLcAZNOAObbu8mufsOHyoKew079n8iNN1WfhQU2Rdn3Y873zyQGTlx/7U76sueIi6pqbIc4d2kS3LYcSn04eZhl3+5vU+1RRFKoG0dF1pWk1hx+WtjvmzM74bOEJElhOpKY4CrqBCO1hHTbEPcFqsNx4DzlTV74vIjcAZIvLXwNVE81c4kfWpk/Uw5H0apT24rmqKogc52V8+sYztszu9fRLnPRB58rnE7ZJu8jut4qc1gm2v/1fmUzirkcjTC/tWUxTdp7xrh0VNkddIllKZlXhWveCpMVbVS0XkW8BVRAtuXE2k0vgPSraDnVqQNOvtmugaXQYiTMW/2VMq0zM2XUCTc1lv/BUTU/PuxC746hlnxWsOMBal69IbMuO1G147raIHpm7vpqhnbMbt2hC6pmuTJUeZl2Za/IPqGWfFWxYfPWMb27Xbx4Kk207/mHPlmD7uE63obzrhDl1EWecCqOcO6urI0Vct1RD7Iq/yVimrqvFWcfoYdsrkYRTyW0RV9UZRnGZ8vly7FyYS3KE7ia8b3eUJttseoBkEZvm36Ra+VBnqMh4ld+gEEemJyNUi8v14vzF36Kbw1YPpsmt0X4fUbbUEZvnX+UIIuDHUZdzBlT589IxPBDYY+5XdoQOBQKAVVN23lqjVGIvI/sDrgS/G+8KQuEM3uR7a1Phkp1UWo8pQfzYPESNRvzvYM67bIv098OfAqnh/HTXcodukkUGBmC6rK0aZof5sHiJGon53cHL5OlNovgF4SFWvrHj9wFaHDgQCSxvtq/PWFnXUFC8B3igidxJ5mbwC+BwNu0P7wHXyeJ/st3LdQNJdSqyeyq9Ho25NMkiGTkXUQTVFnSk0P6qq+6vqeqL5O3+sqm9jlxsglHSHHmUe37GFuQ4ugjhK7JidGbQIgWGhg6ZtTYxifQTP7tBZ+y6uvWnnkjkBqrqIlp3zwEyzqvuoq3toFTdal/xUcXf1TZEM9vSYVeancE23Spgy1w6LO3RCmlt8t92hu2fm6aUxVtWLgIvi37cDh1eJx2WiIFd36Dz356K4TPLcoYvcOLPis/OVlx87zax0izyhXNyhi+J1dUVuii64Qxe5J1dJc5jdofPk9TVRkB3WC7PdG8AbCnfoQCAQ8EoHHaBCYxwIBJYeHZybIjTGgUBg6TFqOuPYrG0zMAfMquphIrIW+AawHrgTeKuqPuYSX5r+qc7gWZlBgaYH8IriXD6xLHNy8yIZJnrjC5anKTs3b15+XAcci3SNeTLl6YLLDNi66Har0KUBvKzlv0x6Yz36c7OlBvDq6mTLDkLaU7K2PoDXQcsmHz3jl6vqI8b+ScAFqnqyiJwU73/EJaKsicDLzGecFl9W+C4N4G2d2TG/DM+Wme2lBvDSVj9xGeArO4Bn7ttxJQ1AGq5zMRcdKxrAM2XwOYBnL0KbRpVJ6+1r07CvTeTIG8Czw3RxAG+uPzfYAbxR6xlncAxwZPz7NCIrC6fG2Ca5CV11c/XtRJDMjZzXsA2SvAch7x41bWWRJ4OPh7juHNFVwpexivFBU/HmpTdIJxyd7V6bUrcxVuA8EVHgn+NVVPdS1fvj8w8Ae7lG5tJDKvPZmmbuUyYu13iqkCd7f2429TPO5TO8jOomyYuLOZiLCqlpynwKz5dlRRnNsvCppiiqh67xudTXMmoK13TLXFcmD0FNUb8x/nVV3SgiTwHOF5GbzJOqqnFDvQgROQE4AUB6q2naJdrXzWyrAbJVMk2kXaXCt5H/rJeCT9VDEU2lU+flUOf6gEUH1RS1ptBU1Y3x/4eA7xA5ezwoIvsAxP8fyri21bkphnFegqT32eR0n12kaq+/65j6/Cq62VHIf2eeww7OTVH5KReRFcCYqm6Of78a+CvgbKI5KU6m5NwUwQMvXQ1hT/fpMtDmkm7ZAbyiwZ6mG4th98DL+sJZah54efIV7YcBvHT2Ar4TzSfPOPB1VT1HRC4HzhSR44G7gLfWF7M+vt7Ibb3Z0xqTxKrE1+BelQYrfC7Xo01VSyCHUdIZx3NQPC/l+KPAUXWECgQCgSYZRWsKr2SNyCY60x67jN2zehhlPlPzLC8S8ozT6/QSy44+91Xne8R5DiJT45OlnEfsY1ky2I4Eie1tm728KtYUNssnlgEsKqO8Mq06sFnHcsKnNUWRg0WZdG1cnYKK0mrdmmLE1BTeydI7mQb3beuME31tns64jOqiis7YDr91ZkemznD77M5UeerqjG1b26RcXPSpvvChM85qcPNeYFV1xq7l0bTOuIyzVFtOH0FnvJi6C5LuLiLfEpGbRGSDiLxYRNaKyPkicmv8f40vYQML2XvFGvZeEYo3YegXyQy0Rwcnl6/VGBMts3SOqh5CpD/ewC536IOAC+L9ckJ1yQSmJaqYrz2w5TEe2PLYokbI5xI4g7oXVdKd6ainpk8meuOFdaXKS6nt+zzw57uv7ltL1DFtWw38BvAuAFXdCewUkWOo6A7dG+stmgAlT3dUFL6MHqqMHq3Kp2hhnAUWEnkymGoLU7fsEo99rEx+mlRLVNGt9h31onVksfWvPtIro2/NmyAoIVG5ZN3XKvrdIurGmVe/m7BA0dkRsqYADgQeBr4iIs8DrgROpIY7dDJ5iH0jkjf9TH9uge7SnmwkCZ9GGZ2x2bOcGOuxfXZnpi6sN9YrNXeBD53x1PjkouXSk/Brpleyafvi1bbr6oztAa6kd2bmfRh0xlUG8Mw0zAFkOz1zP0+GvPib0BmbddS3zthmeHTG3WuM66gpxoEXAF9Q1ecDW7BUEqqqRPNXLEJEThCRK0Tkin5/YeNhfzJtn93J9tmdziPCLufzmIsb/bn+XKFlgq9JjMo8BLZM5stj0/Ytjagp7MZ/Zm620Qmcqnw2u+R768yO1Huad5/T6GuxR1wTLyeXcrHLwaU3XRWXcugkHVRT1GmM7wXuVdVL4/1vETXOld2h550ahvUG16Duy8PeXze9G+umd6srVmv3YvnEsvlea1a6RbrQiWFbLr4CLvejq7Mc2qyYmGLFxNRgEh+lxlhVHwDuEZFnxoeOAm5klzs0lHSHrluJBj4o0CEe3fYEj257IrWyD/QhiLEHorJ6rCZFA3S+B/C6MJDchgxNzX1i99B7Y70Fx7bMbJ+fNrZtVNV5a4u6d+H9wNdEZBK4HXg3UQPfOXfoQCAQmKeDdsa1GmNVvQY4LOXUQNyh85w3lippPY9B9UZMqugxi76cfH+eFw0Kt0EbKqKmdMpp6rOuMGrWFN5xMY8pY6LjatpWNOrtKkMZE5yypkBFeSk67uq2WibetvX6RTI01Wi65LMt0zaX88m5MqZtrumWua5MHsqYoXph1HrGvilyqSwyh7Hj8OEOnZxLkyntuqIGwYdpW54JWl4+0uIpyk/eCyvPvKoJXGRoKt2EKi+7KvH7NG1zeW6y4i2iyLQv77rBmrb5icYnlQfwROSZInKNsT0hIh8cpDt03s1fquqLtIG6Mm7UTQ0g5XmSZaVXZLq2esrvIgUueZ/ojZcunzJlmoT1dR/S4mhyAM8ctLMH8Oz9tGubQvvqvLWF+BgtFJEesBF4EfBe4BfG6tBrVDXXA298cj9nIVyWKk+jjheP6XW1anKazTu3VYqnDHm9QF+9AzsvaT0qO+2kcW+jDNqmat0qm0YSf5Y3X2AXac/B7M6Ntd9Kjx/3cueHaPfTL8xNT0R2B74IPIfIr+L3gZuBbwDrgTuBt6rqY3nx1J2bIuEo4OeqehfR6tCnxcdPA95UdLGLv33CzNxspQpc1ICtmpxm1eR0ZpoJbTVCWTo4n6qAzTu3LcizqWtM09n1Vdm8c1tnG+K6PbyqdatsGmm/feOrtzvoJb8aU331S2zFeJmjx1dJHwucHv8u7Q6d5WJqHkuON6UzTiwMsnS5rjrjIrqmM968c9vI6IzN0fo6X0Jp6SYMi844a9rMsjpjc8qBNIZVZ6yzfuLxOUdP7cY4tjF+I/BR+1zZ1aFdRmSLRoWrjtC63uS0h7xKBXGxDCiTF1dZ0tJIjrmoYMyHounG18alzPLCFmE3DuaXghnGpZ6Wocq9dDmXVX+qxptHlTLJksku4ybUOWV0wWZbFXOKqp4S/z4QT3P0+OgZvxa4SlUfjPcfFJF9VPX+Indo4BQopzMOBAKB2pSwpjDbqhSSOXrer6qXisjnSJmjJ6tTakdUl+PYpaKAEVwd2t635SyjquiamsI8ZqossuTI+wwdtJqiKGwReT21tONpcvhSUyTHq6opsup3WTVFEW2oKWyViw88zhmfNkfPSTh2Sk3qrvSxAngVcJZx+GTgVSJyK/DKeN8bTZu8FGFWkmE3l8uSf2p8MnVSHtvMapD3oSpZJmI+zceK0k/7HWgZTwN4PufoqesOvQVYZx1rdHXoQbtUuvaoh4GsXoY9XWZm+A65t7pSVdfeRPpt69wDu1C/Kmgvc/R0ygMv7ZOnCwN4Pgb+iuIs+qx2VRfYg09p8eR94trX5dneNtWYlBmIswd6ktU+fMrmEpfvAbwi9UFZmcxnq80BPFf1QtFL0ndd87m0na85ejrVGGfpndI+h+0esm+dcdYE3XYcyZL1rvjQGeetLrJ8YlnqCtFp6dq6xTSSfK+ZXslj256cD5smg68Hpkw8ZU3b6q70kSVfFZ1mWvln6WCrNM5p92pQOuMiebPStVeU6aDO2Bu1GmMR+RDwHiKvk+uIuuf7AGcQqS+uBN4e294VktlDSKlILp+bdXrGruvIVTW5Kds7WSBrTppFcwKnPSxZD4Z5/LFtTy548QzCc8ylB1l0PKt87HUEXeIqGwaKTSNd7Ytd6s/8/4J1JV3jzaPMvUk7n3kfG6pnXWyM68xNsR/wAeAwVX0O0CNy/vgk8FlVfQbwGHB8XSFNdUXVAbw6ul3TC6nJSdnNfOYNMvnCzkte3GMizPXnOjExfVO0MThsz81gk6aaK3O+Kk3FW5fGxmRU3LeWqOsOPQ5Mi8g4sBy4H3gFkXkHOLpDF5E0Qonxt2nq4krZimanmWDOBdzk4F1WTyNRjWRRxn3VdvDIK6PeWI++7nKHXjO9snODl2l5t19g9vJO5nHf7tBp8rTlDl0kx7DQ1AtC++5bW1S+S6q6UUQ+DdwNbAPOI1JLPK46P1Z5L7Cfa5xFOuMsF0/zmjw7W1edsaljS9I0P/1MXVyPchYePnTGaS6qWbq6vHSz9OzzPbb+3HwYO4+btm9ZtEp10z2rIjvjNJ2xHT7LUiTruJ1GGfWBa71w0RnnXWOHs3XRLs9NVrxlKaqHZriq4zs+6M92qyMB9dQUa4gmBToQ2BdYARxd4vrM1aEDgUCgSVTFeWuLOt8vrwTuUNWHAUTkLOAlwO4iMh73jvcnmlpzEWXcoavYFhdZCfhIr4q6xAd5efNhh+0SR181tzfZVcoO+DWR1ihR9EXaVUZqAI9IPXGEiCwXEWGX58mFwFviMO+khDu0D7K8x7pOoh4YRq82gHXTu2WeS3TvCbYOM02HW4Wm7nude5JMPu+rsWrKS7AN70MTX/e8KtoX560tak0uLyKfAH4HmAWuJjJz24/ItG1tfOz3VDXX3ipMFDQaJHMjD2q+4zBZuzttTKTfFD4ml7/7sKOc25ynXnFBKy2yl5U+6hIa49GiyMtr1NKtw1J5gfi8Nz4a47te8EpnYX7pqh+10hgPr81LoLMk5ndVG5msB7cozmFriMG9Z+rLmmBQL6yu3Zv+XPd03KExDjRCnWkPs8IXNVzD1jMuI+8gXM27QFP3tE1dsCt1p9A8UUSuF5EbROSD8bG1vlaHHrYR2rq0PYjikyzb5iInlaVMlxrGrta9xpw+OmjaVsfO+DnAHwCHEy3C9wYReQYVFuLLosqNyFtYtA5NV9YuPghlyLM4mJmbZc30ynnvtzXTKxect/ebkKEOdV3pfdYdl8V7q6TVtju0r3telZHywAN+GbhUVbcCiMhPgDcTOYIcGYc5DYeF+HySmDdtmdleuXKlfRolD7o9cYmvz6gu9ZKqUKRC2DE7w+7LVkRhLTvmcem2OV+al5rr/fI9OOcS3zDUpUHf836LPV5X6qgprgdeKiLrRGQ58DrgACosxBcIBAJt0p8bc97aonJKqrqBaIa284BzgGuAOSuMEk2vuYim3KGnehNM9SZq9Q7KXDsMvZA2KPp0XjY+wUx/jpn+HOuWLXQQsfdHiUSt4Etv7jOupYyq+9YW3uyMReR/E00MdCJwpLEQ30Wq+sy8a33ZGQ/baHobpJmDdcHgP9EZPrbtSedriu6vb5td35PTdFWGpmyd7fvlKy8+7IxvfPrrnYV41s//o/t2xiLyFFV9SESeSqQvPoJo4qB3UmF16LqEhngxaQ9ZF5wMkkbYp3mX7/URB12f2upcNFUfqkzS3xajpjMG+LaI3Ah8D3ivqj5Ow6tDF3Hg6r05cPXe3uNt+vNw2K0piuYaWDO9kj2Xr2bP5as5ZM0B88f7qvzK2vVeZGhrXo8y96qOmiLL8WUU1BT7rlw70PS7aNrWKXfooGbwR9Zab13FRd6i+pG3jl2ge7jWUVuN4kNNce36/+bc0Dz3zu91X03hm9AQ+2PYGqVE3rwGt6h+DFueu8AgO0Cu96sJNcpcvz0rCVe6J1Fgni5Ml1hVhqpy91UznXaKVCHDrurJI2u5qLIUrdLsm7z6U/WcD7poTVHYGIvIl0XkIRG53jiW6vIsEf8gIreJyLUi8oJKQnXUNbNJ8tyJy15bVHZteFvViX/zzm3zulEzL0u557t1Zsf8CtZF97douaM2yatrVc/5kUuct7Zw6RmfyuLllLJcnl8LHBRvJwBf8CNmIBAI+KOLA3iFjbGqXgz8wjp8DJGrMyxcAfoY4KsacQnREkz7lBWqq8uGN4lPJxWfZTeoezHXnyttqrYU6sxSfDaaYFh7xmlkuTzvB9xjhHNaHbqpyX0Cw0vS6CQ6ZJf6MQomXz4Yxsa67XunJba2qF0CqqoiUlpmETmBSJWB9FYzNrYi1UMnb8lul2Xn064tisskOZflSVRWt521gGMZ+dLSteNNJkyaiXuY5vnEHjcZpXbNT9Gy7ub5Iq8u+16b+7aJWrKM00G778etj29MjQdg5eRUJWeSIvKWtrfDVEmzqB7DYjMwl7KvUr/r1mdbjoS5/tx8vUvqo+kJOtefWxBHci4J69sTsYvWFFUb4wdFZB/D5fmh+PhGosmCEkqtDp1W0Hmf4EXhiz7fi+Kqe10edfNaZP6VNdjVV10081zV/OSFLTJHystPluy3Pr5xUSNr/jZdq32ranyEKXOtfcwuk7RrkgYrKfsq9dtnfbbrgF3vzPP29Yuu9dzb7+Di0JXVFGcTuTrDQpfns4F3xFYVRwCbDHVGIFCbpJe0FC1uigj6ZHcUcd7aorBnLCKnE81PvIeI3At8jMjF+UwROR64C3hrHPwHRFNp3gZsBd7dgMyBQCBQi34H31mFjbGqHpdx6qiUsAq8t6owQWecrZssqzN2SbeozOwwZXTGTZDIkFU/TBlGTWecd40dLsl72n0tU89cyJO3aPyh6rPqg36LPV5XwvBzIBBYcsx1sDHuxJCi7epZRR9YxitpxcTUgpHeMRGmxifnLRBszNnA8kxwkut7Y71FM4itnlqRGX8iQ9p1eSQy29f0xnqLzpllunpqBaunVizKT1oZZs0SZh+bGp9c5DVn6nbN2cvMLTln1gFbJ5yETWTOYsvGixeUgR2XKYfNqsnpTF20ff/Nde1sL0Hz95rplanekcm2anJ6gSx5975IfpOp8cnM5yHvHqfFm1Znk3pqyptWz+xw5u+J3jgrJqZYMTGVKqcZ1jRr9DVO0EWdcVV36N+OV4Tui8hhVviPxu7QN4vIa5oQOhAIBOrQL7G1ReEUmiLyG8CTRJ51z4mP/TKRnP8M/KmqXhEffxZwOtGK0fsCPwIOVtVcVypfK30EAr51i4HmKavf9zGF5g/2OtY5wdc9eEY3ptBU1YtFZL11bAOALP5kOAY4Q1V3AHeIyG1EDfNPXYQZ1ABeHmUG8HpjvUIX3kEN4LnIMiwDeFky9MZ68/apqyan551FqsSblUYYwNuFWd7DNoDXpvrBFd8DePsBlxj7Tu7QCYN0+igjV1YatlF7GnmVqqrjiWscLnGXibft3mfh/TbKf/PObc49rqIwXXD6KHM+OZdZT0vUs1wZcpw2XOJq4ll1pe+5LRaRHnAFsFFV3yAiBwJnAOuAK4G3q+rOvDgGNoDX1OrQbVJlMMHFMH8YnBm6KGNab3GQyxR1sYwCEXOI8+bIicAGY/+TwGdV9RnAY8DxRRH4boxLuUOr6mGqetjYWP4ouUkVSwufuHyy1mUY9J3DICNEbrXmPA0u+Kpfo/DSHVV8DuCJyP7A64EvxvsCvAL4VhzkNHbNbJmJ78b4bOBYEVkWd9MPAi7zmYBLz7KIOj2lqmkP+iWy1CnjoNPWi2ZYXmguDFvd7os4b+ZXfLydYEX398Cfs6vtXgc8rqqJHsdJXeti2nY60QDcM0XkXhE5XkR+M3aNfjHwHyJyLoCq3gCcCdwInEO0YnTt9dOTT03TFrlOg+qyplZamjZlB8t8PXx5MvlamsfOmx3v8ollnXsAi2y0+6ocsuaA+dWpTRWG64ritu1zHkXn2yq/NdMrG09j2F4sWmYzvuLj7ZQkHhF5A/CQql5ZV6ZOrQ7dNsEMauni01060B5jIuzccW/tt9g39nmb883/nfu/lpmeiPwt8HZgFpgCdgO+A7wG2FtVZ0XkxcDHVTXX76ITHniu+O5JjMpgWsCdpEdrD+6V/dIKaqfB4OsFOivivOWhqh9V1f1VdT1wLPBjVX0bcCHwljiYObNlJkPVGAcCgYAPyqgpKvIR4E9iX4t1wJeKLhiqiYKa+qzM+2QNn7LDSdY9NccLTIcFl3EEk1AvhhvfdsYAqnoRcFH8+3Yihzdnqs5N8X9E5CYRuVZEviMiuxvnvM9NkXwS2pMJ+SLtwUpLMy3MIAgDeOmYE8pkNZYHrt57frDOVFm8cM+DndIoM4BXdC+6NIC31NQuXZybwkVNcSpwtHXsfOA5qvpc4BbgozA/N8WxwLPjaz4fe6bUItHtbp3ZMV9pmu6Z2GkmmA/YoHpHWcsSFZ2zsRuTvIcxKYekEdo6s6NzvcMtM9sLw9yx6QHu2PQAsMsGGeDyh29hzfTK+YarqGEyr80i7V6Y9ceesSxr9re6mMtRZeHT2mcYaEFNUZrCxlhVLwZ+YR07z7Chu4TIuQOMuSlU9Q6iFT9KddW7iFlJt8/mejQOFVnrjGU9mH1Vp0aoi7g0bo9te5LHtj3ZqNrKbKDtl4ery3KgPn1x39rCxwDe7wM/jH/vB9xjnCs1N4ULg36Dt5X2ID4Zh/0zte6cC+ZXV5YKom4ZuXpwDvu96DqzJba2qDWAJyJ/QSTv1ypcewJwAoD0VlPGJTqLUbId9ZWPvJnOmp6MpUiuttMswpTFXuo+LUzdNFzCdbGcRgHt4LuucmMsIu8C3gAcpbs8R0rNTQGcArucPupOoVlnWr6snkhyLk2mMi62Znx2vpLjSW9srj+X2YBmpZsVb3Ks6LxLvHkymdMppmFfX6VxKSODjxdzcv1Eb3x+atSsOLMaTRc5hnUKzSJ5y7iftz2FZpsDc65UUlOIyNFEvthvVNWtxqnG56YYZeb6c4XzIXcV13mcBylDnXjLLomVsNR6tK5WGYMuly5aUxT2jOO5KY4E9ojno/gYkfXEMuD8eIL5S1T1j1T1BhFJ5qaYxdPcFIFAIOCTLr4iOzU3RZnVGaqEb4Ku6KkTFUcdS4e8vHQln3lM9MYL85+nTkhIU00lHLBqDzY++ajzgGDRIN0wl3dT2Hm376uPZZc+99Tfcy7cE+/+t1Y0zJ3ywCvbsJrh7VHwNL2rK8P4IPgwN6trjVBElq6yzfJ2NVnLCrfxyUdZMTHlVFenxidz7b6bLu9hxc57E6aUXTTO7FRjXIfkBvpulIoaiq49NF1+kTTtcu6iMza/IMxeskuvOgm7eec2py+RUbJJHzW6+IRUdYf+X7Er9DUicp6I7BsfFxH5h9gd+loReUGTwrdBVxu2LFzkHeRSRE3iMsBmOq2YNutlX+JJPKYLtk3WvRjV8i+iS/keVqePU1nsDv1/VPW5qnoo8H3g/4mPv5bIguIgIhviL/gRsz7BiH4Xw2y1kccg8pQsfFqGYfViLItdLl3K91BaU6jqxSKy3jr2hLG7gl29/mOAr8Z2x5eIyO4iso+q3u8iTF07YzuOYbMzdrX/LGtnXHTeh51xmsy+cZEhL2yddBPS4qw7VjGqdsZ58dXxCfBBF7936zh9/A3wDmAT8PL4cJY7tFNjnFXRs/aLwhcNyrg6IVS9Lg+XvLrK4BqHS7pl4m1bhVMkg6ursY90ber0yquUrUtdybqvTYyB1M1DmWfVB7MdbI4rz02hqn+hqgcQuUK/r+z15iJ//f6WqmIEAvMMUr+f6J+TXpyr88OwM6z51BJbW/iYKOhrwG/Fv0u5QycL/BXNS+Fyw+3zdSqI67WDqoh5abYlz0RvvHMPYdq8vfY9yhpEcp0Hekxkfi7novz/0m57OcXZBYa1Ua1KF3XGVd2hDzJ2jwFuin+fDbwjtqo4Atjkqi8OBAKBtuiiNUVVd+jXicgziV4cdwF/FAf/AfA6onmMtwLv9iGky+en68CHr/TqppGGq+xdsHu2R8WL7HTN83ZYVxvfIjZtX6zucnUgyHPOMAcD+6qFE/gnYe/Y9IDTJENl8D2QleBTV+yCr3telX4HdcYu1hTHpRxOXVwvtqJ4b12hlirDZtNsUjSA1YbZWVPlVyfeUTQh9MGgy6WLT1o3LLA9MswNWhZd9qpLKNObt3tEXbE9bYIik7M68Q0zg87HSFlTDIqqAw2+Bid8LPjpQpbtqc9BlrzVLLLskbvkRWVTt2yWTyybv79NDGb1Vdlz+eoF6Y0yXR4QHEprijR3aOPch0VERWSPeL9xd2jThXUQlFnwsw5ZTia+9I5jkr08fVY6fR3eNfBc2DqzY/7+upZzmRfTmAiPbnuCqfHJwkmERpEuWWwMqzXFqSx2h0ZEDgBeDdxtHG7cHbpqz6xOI2ZWoLy5CJqiicEa02vMJu2hSY6VKf+2Hz57tWVbluR/Vq9/1eQ0qyanS5kOlnkx9VXnG+GtMzvYd+Xa3LiHnTTHjTreiT7po85bW1RaHTrms0SrfZjSHkPsDq2qlwC7i8g+XiSNGUTPzKxAg54/2SdlesbJMZfyTxrrtr9its/NZJ4zrSGyev2bd25j885tjVqrmL3h+578xYKX+6D1qE1SVbXVVJl0UU1RqYRE5Bhgo6r+TBa+uWq5Q4e5Kdqdm6KozOwweTKZYZt6WRbJYI7Qtzk3hRmmbJr2REOuJprDMDeFfW/KPMtNz03RxTXwSjfGIrIc+B9EKorKNLE6dFP0xnr0R1RPOkrUvU9N2fDmpWemFepZe8x10JqiSs/46cCBQNIr3h+4SkQOp+bq0IFAINAGQ+n0YaOq1wFPSfZF5E7gMFV9RETOBt4nImcAL6KkO3SWLi/rs6popqgyM0Hl9Ybsz27X6/Ioq5d0ncWqiveeS37S1DVt6zgLZTfuk08bXpe46qQ3/99afSQNl967HW/e7zLx5uFSZ/POl3lWfdC9priiO7SqpnrgUdMdukjvZIcZNZ2xGf8gdMZF17nqjJuijAxVdMb2fXW5V2nXliXtniRu1FmNkm+dsUtdSMNVZ5x23WB1xt1rjqu6Q5vn1xu/leAOPbRUebnUxedAW11cvxDaYK4/F3TIDTISA3hNUvbzPK2X1ISaoup1eZT9rKuqpkgrk7xeVZlGqE7DVKWnU0YGH41mGRnrpJeVrzy1hW81hcu5PIZNTdHFAbyhc4fOoys9LF/4cJqoWyZVZSi6pq/ZNshZbsJF7sO+e/V5MrZFIsOqyWkv7tNtu7Ln1Z+q53ygJf7aourq0B8XkY3x6tDXiMjrjHMfjd2hbxaR1zQleCCwlJhTPx/Wg54trSuMlDs08FlVPTTefgAgIs8CjgWeHV/zeREpXj/dFsp6K5Z5S7btguuLZOUMe+DCpWdm93bq9ErzKOMmbMdvymjLa+9vndmReh+L5nLojZWuao2T5KNu/U1cqNdMr0xd0cQkrwedZ6XRxHOTVdcS9VmemqnJr5IkfpetLSqtDp3DMcAZqroDuENEbgMOB37qcrEPa4q0sFnhu2RNMWPoB8taU9ieZ2nxu1hTFFlpFFky5GGaB7pMoZn3AGfJ0EUPPBcZiu6JyWPbnlx0jR1u++zORXEEa4qFdFGhWUdn/L54ZrYvi8ia+FiWO3QgEAh0hqGcKCiDLxB54h1KNO/E35WNIKwOHQgEBsUc6rzlISIHiMiFInKjiNwgIifGx9eKyPkicmv8f01uRFRsjFX1QVWdU9U+8C9EqghoaHXoQCAQ8InHnvEs8GFVfRZwBPDeeOzsJOACVT0IuCDez6XqrG37GG7OvwkklhZnA18Xkc8A+xLNa3yZa7x17YyLzi9FO+Oy6bZlZ1yFtu2My8TVhJ1xmWtMHXkX7IxddPaDtDP2ZbIWt4P3x783i8gGItXsMUSeywCnARcBH8mLq+rq0EeKyKFEevA7gT+MhblBRM4EbiR6Y7xXVYMtTcAbXfLY6xJNDHLVoQsy5FHGZM2cYTLmlHiiMzvceuD5wKXAXkaH9QFgr8J0tAOFlszaljZC7GoBUWQZ0HVrit5Yb4E1QBlrCnMJnzGRRXFlpetiTZEWR5pMaeftsGUe0Kz5GmzLi7xy6II1RdX4s+JLzNYSi4k0uQ5YtQf3bH6klDVFVbO2qtYUdhxlntXZnRtr2+D95lP/m/ON+s7d3ytMT0RWAj8B/kZVzxKRx1V1d+P8Y6qaqzfuhDt0XkVuS02R2Ki6mFk1oaYomoMgTwbT/ravmhuXHY/dwJXJT1Nhs8IX3RuzgRpVNYXLunn3bH6EfVeu5b4ndy3QU+a5MVk+scwpzbpqrLbVFD6tJERkAvg28DVVPSs+/GCizo1XO3qoKJ5ONMaub9cme8ZJTzKrd950zzgrP3aaWekW9XCyesYz1vwHdeyMm/40LWPrPKo947Rr7HBjItz35C9K9Yyz4t0+u9Ppa2nY7Ix9zU0h0aTuXwI2qOpnjFNnA+8ETo7/f7corsqrQ4vI+0Xkptic41PG8cru0H1NX3stYaI3Ph8medjsa8x9+3zWvn0uLc0sOe3rijY7jjz50tLsqy4oBzt8b6znnK5Lfsx4TfJkaIqicinq/QGZHmx5Xm0ueaxTBkX3pOiarGcmOXfAqj0q1bMq9dk1LvuaMs+qDzxaU7wEeDvwCmt6iJOBV4nIrcAr4/1cXHrGpwL/CHw1OSAiLycaLXyequ4QkafEx0136H2BH4nIwa6DeEVv17xeXHKNb51xkmaaTHnXZWHLmSefSVY52OHttcby0i0qMztekzwZmqJM7zyrZ5x4sLket9PIymPXesbmvczSH6fFv2Q88PzF859AVkaPKhNX1dWh/xg4OXZ7RlUTfcgxxO7QqnoH0STzhxMIBAIdoosTBVXVGR8MvFRE/gbYDvypql5OZF93iRGulDt01mdT1n5R+LxrXeKqe10eLnl1lcE1juR8Xq8qq6dUVt46Otsy12b1xLx+0jrEVSc9l7K1V/5wqStp9zXNIqVIFhey8uDaoy2qz76/utqcGtOVqo3xOLCWyOPkhcCZIvK0MhGkrQ49yAG8QZu2lfl8zGtQywzg2XEXxeuqIkiTvwxlrl0qA3h5Jn12uraawvxtq5faUlMUqbSyZErLiw98TUnqk6qN8b3AWfEyS5eJSB/Yg7A69JImmQozr+cV6Aarp6IpCPJ05aPMUK6Bl8G/Ay8HLhSRg4FJ4BGCO7Qzg1RT5B0rE+8imTw0wnk92jJlNmpqijLn89QUyW9zKs5B1Oc8+Vz26zKUaooMd+gvA1+Ozd12Au+Me8nBHbpjpOkIu9CDzZKhjh66SB8aWExftbFyy1PvDZouyGDTKXfoLLp0E33qIu14E8rG35RMZdKpes4ndRqVJmSsEqerSZvvwdPEzrottUWd8vbhDv3S/Y5yTvz/brygdnoudMIDL8HFVnHQA3iu12XhMoBXNFiWl26ZAbyiMrPDVB3s8TmQlidDnZU+ihq3onBpddc1/TJ2xnn1J0+moucmawWRIlwH8NKuG6Sd8SjpjAOBQGBo6aI1RdXVob9huP7dKSLXGOfC6tCBQKDTdHHZpUru0Kr6O8lvEfk7YFP8u5Y7dCAQCLRBF60pqrpDA/MzFr0VOD0+dAwV3KHHpJllwsswNT7J1PjkQGUYBIlVwyiwFO9fFsm8x3U5ePf9vcRTRNv3TlWdt7ao+yS+FHhQVW+N9yu5Qxd5j7WBPVn3UiFtwp9hZanewzS2zuzwcl9vefxeD9IU0/a9G8UBvOPY1SsuRZo7dCAQCLRBFwfwKjfGIjIOvBn4VeNwcIcOBAKdZyh1xjm8ErhJVc3vmLOBY0VkmYgcSEl36DZpUle6VPXPg8aeAD/QDKNQv/tafgL9pnExbTsd+CnwTBG5V0SOj08di6WiUNUbgMQd+hw67A7dhPtn0hhsn90Z9JcDJjTMzZHU72EuYy3x1xYj6w7dxny6g3LT7oLrcdtpDRNNzavcRQYxz4kPd+hffsrhzjdmw0OXBXdo81hamKru0MmS7nluwPa5rAlPXM3y7NWnm5rPOC1u87xPd+is+JqiyB26N9ZbUL5pYavIWNYduup8FGb8rnNUpMmVN59xmXrmQlLe9uT3RXEN2h26izrjTjXGbTEIFYK9hlzAP0VlPOq91EEybPW7i9YUVd2hDxWRS2J36CtE5PD4uIjIP8Tu0NeKyAuaFD4QCASq0MUBvEru0MCngE+o6g/jZak/RTTn8WuJLCgOAl4EfCH+70RaxrNmrXIJn3etS1x1r8vDJa+uMrjG4ZJumXjb7mkWydCUysRldr466VUpW5e6knVfy9QzV9LUK2XyUOZZ9UEX1RRV3aEV2C3+vRq4L/59DPBVjbgE2F1E9vElbCCQR5Mvh7Z7SWXpihdlUk5dkScL1b7z1hZVdcYfBM4VkU8TNei/Fh/fD7jHCJe4Q9/vEmnRAJ7LQITrXMN5caWFyxvAK0OW67evATz7eG+st2BgZUwkczCx7ACey5y6WVQZkEmbPL7MAF5VinrcZXrkeXU27VgbA3hmWfmaz7ivyqrJabbMbJ8Pm9S7pD6G+YwXUtXp44+BD6nqAcCHgC/5E6kZutyraZK6AytNTeKU19Pseq/KpkzdqqqL9HUf8ixtfLNlZju9sd6CRtisj+Y5m7xzPujiREFVG+N3AmfFv7/JrpnZnN2hReSEePDvin5/S0UxAlWwH4o86ppqVSErvSKZh21EH9w9QX2pSdrulCR1bd30bpnn8q5rTC7tO29tUbUxvg94Wfz7FUAya9vZwDtiq4ojgE2qmqqiUNVTVPUwVT2sjUmChq23ZVJH9rTeRdO9DpcHvkpPr0jmQXiEVXGrN/PehQVUm3o2zPvx6LYn2HvFGvZesaaRtMoylNYUGatD/wHwuXiyoO3Es68BPwBeRzSP8Vbg3Q3IXIlhGFTIoo7sab2LLvQgq1TyLvaMqzSmXVOZNSWPfT8e2PJYI+lUoYvWFEPhDl2Gg3aPpk++9fFU7UhlVk1OA7B55zav8SYkHkxQ/uHoglvy8ollbJ3ZkXl+zfRKxmVXT+nhrZvmf++7ci33PZm6fkEp2lpyvgx17muWLEVxVZG3bdf+F+55MJc/fEula324Q++1+hDnjD646aal5w4dCAQCbdBFa4pO9YyL/NvrmLYVmcuMmmnbiokpgHnToqqmbWlppMmUdr4MyTJByZwhaXEVmbatmJia/3Jp07TNDFMlTRfTtqz9NLnyTNtsiu5pEXmmeGZds1UWfVX2XbkWgPue/MWiMkh08WlmcD56xmtXHeR8o36x+dZWesadaowDgbq0/bkdqE/ZF6ePxnjNymc4J/jYk7e10hhXnZvieSLyUxG5TkS+JyK7Gec+Gs9NcbOIvMZFiIneOBO98dQR9uRYcjztt3lN3nnXuNLCpcmUd11efGnXZeWnqByK4s0775IfM0yeTE0Ojpr1o0iGJjzAXPJYpwyK7knRNWn1046jSj0bE2H5xLJS9Tkvrqw63FflwNV7Oz+rPuijzltbuJi2nQocbR37InCSqv4K8B3gzwBE5FlEk84/O77m8yJSaG80MzfbCROfQDcJ9WNwtDXD4V1PPNhKOglddPooHMBT1YtFZL11+GDg4vj3+cC5wP8kmpviDFXdAdwhIrcROYT81EWYtE8V+5i5XxQ+71qXuKrE44pLXqukWSRLXrpJL8WVtlUBZcrMp2xp+lif6VWJz6WuZNXvMvXMlbp5yCvjJqxkuqjGqmpNcQNRw/vvwG+zy+tuP+ASI1wyN4UTyWfIMA3g2TIW0dYAXl66VQfwbLJkqEtWg9fVuSnMMGEAz30Az1wlxC4DcwDPPO/rnnbRzriqB97vA/9dRK4EVgGlv2WqukM37T2WlWZCk7rRtkhcTV3ykuhgkzIoo7urqufLeuC66PRRh7IvcR8NUds9wqouz8m5phY+nev3nbe2qNQzVtWbgFcDiMjBwOvjU85zU6jqKcApsMuawuzZJNiVxzxfFN6XmsJMww6XJoMLvtUUrj2HvHRdPgddy8zlvInLWmpFZbZqcnretK0pNUVWGdVRVQU1RXYZb53ZwfP3eDpXP/LzSnJl0cWecaXGWESeoqoPicgY8JfA/xufOhv4uoh8BtiXaJL5y1zjTXprrmoKs3c3KDWFaw/TjM/OV5Z8Jj7VFFnH7M9FM0xaD8anmsLlhZamejBlMKdrbEpNkSVn02qKvGvscHlqijL1zIUiNUXedVky2fXw6kd+7l9N4fFlLSJHA58DesAXVfXkKvFUnZtipYi8Nw5yFvAVAFW9QUTOBG4EZoH3qupwfTsGAoGRx1djHFuL/RPwKqIxsstF5GxVvbF0XEvZ6cP32zYwWMr0hn32nAPtMdEbZ9u2u2oP3JRpc/KcTETkxcDHVfU18f5HAVT1b0sLVcberskNOCGEDWFD2BC2bljfG9GslFcY2wnGubcQqSaS/bcD/1gpnUFlMCXDV4SwIWwIG8LWDdvm5rMxrmraFggEAoESFmRFhMY4EAgEqnM5cJCIHCgik0TTQZxdJaIuzWd8SggbwoawIayHsK2hqrMi8j6iKSF6wJdV9YYqcXXCmiIQCASWOkFNEQgEAh0gNMaBQCDQAUJjHAgEAh1gYAN4InII0TScyRSbG4GzVXWDFS4ZobxPVX8kIr8L/BqwAThFVWc8yvQUVX3IV3xNIyLrVPVRx7BDk7cy+QoERoWB9IxF5CPAGYAQTSR0Wfz7dBE5yQr+FaJZ4U4UkX8lmj/5UuCFRCuOFKW1LuP4WmtbB1wmImtEZK0Vticifygi/0tEXmKd+0vj93gc7hwRuTbefigifyQiE9Z1T4uXtPprEVkpIv8iIteLyDdTJvNHRE4WkT3i34eJyO3ApSJyl4i8rEbedhORvxWRf41fdOa5zzedtzL5CgRGmgF5rdwCTKQcnwRutY5dG/8fBx4EevG+JOeMsCcDe8S/DwNuB24D7gJeZoXtA3dY20z8/3Yr7BeBrwMfBK4EPmOcu8r4fTrwBeAIIuPv/ePfXwC+YcV5MfDHwEnA9cCHiYzHjwd+nFI21xm/LwReGP8+GMs7qWTevh2X25uI7CO/DSxrK29l8pVTn95YcD6tru2RckyAFwFvjrcXEVscpYR9KrB7/Hs9kSfWcxxkfQbwW8Czhj1vRM+rGPsvj+/1a9vM26hsg0kUbgJ+KeX4LwE3W8euj2/6GmAzsDY+PgVssMKWabA+DJwD/Ipx7I4Mea81fo8T2TyeBSwDrjbO3ZKT51usffO6u7POGcc2AOPx70uy8l0hb9dY+38B/H/AOhY2xo3krUy+4mNvtrbfAh5I9q2wLyeaSesR4DxgvXHuKivsq4le3D8kevl+MS7D24BXW2FPInqx3QS8J/7/JaIVcP7ECnshuzoIbyfqiHwRuA54/5Dn7WfAmvj3nwH/RTSl7vnA37aRt1HaBpNotFhpUjmSSeaTynG0FfZDRD3cu4APABcA/xJX5o9ZYcs+2PsD3wQ+Q7Riye0Z8t6UcuxjRI3WrcaxS4jUKGPGsTHgd4BLreuvJHpJvDCudIfFx5+B1eOPj78/rpivAD5ONH/qy4BPAP9aI28bTHnjY++KH767aubtcCtvB9l5q5CvGeD7wJeJVFhfIXpJf4XI4N4Meznw7Pj3W4BbgSPi/atTymF9SnoHsvilfwMwTfTC2gzsGR9fAVxvhb3ekmdd/Ht5SlkMc96uAKbj3+Nt5W2UtsElHD3IRxC9IX8r/t3LCLsvsG/8e/f4Bh2eEq7Ug21c90aixuaBjPP/hvWSiI+/B5gx9tcD3wAeJuoB3Qo8FB870Lr2KODm+EH5dSL1QBL+TRlyHBnHdTXRy+gHRDNKLfqcK5G3TwGvTDl+NAtfNEneHorzdkvFvB2Tk6+rjHz9YVq+iF5eFwB/bBy7IyNvP7P2nx3L9SYW9x5vJX6RW8cngdusY4nqrBfnyXxB2Q3W1cB+8e8LgSnj2huGPG//Ray+IOpMJb3kqZSwjeRtlLaR88ATkSOJ9JUHE72h7yFaOPXLqjprhT2EyJrjUmAOeLqqXi8iR6vqOVbYwwFV1ctF5FlEjdVNqvqDDDmSgcPPqervOcr+fSI9WuHCWyLyUqKe53Wqep517kVEPZ4nRGQ50YvpBUQ91v+tqpuMsB8AvqOq9xSkNwkcB9xH1GgeDbyEqCe1wKrFCLtRIwuYt2WFjcM/jeiFfADRfbgZ+LqqPpEhyxjRi/dNwEeIViR/Wkq4K4A3qOoDxrH9iXpoT1fVVcbxjwJvJRpYTsriACJLnjPVmJ9WRE4lashWAFuJFlI4h6gTsEpV32qEPZJo8vFvA2uJ7sO5RC+pc1X10wPK21OJvmrq5O25wL8SqSsguscXA79CNK7y9abzNkqMXGOchYi8W1W/Yux/AHgvUe/tUOBEVf1ufO4qVX2BEfZjwGuJGvfziQY/LiSa3f9cVf2bOFzaBCGvAH4MoKpvNOJ0DhuHv0xVD49/vyeW/d+J9IHfU2OpFxG5AXieRn7zpwBbiBqDo+LjbzbCborP/5xokO6bqvpwSvl9Lc7/NLCJ6GH9ThynqOo7K4Y9kcha5mLgdUQ9yceB3wT+u6pelFJOybX7AZ8lUoOkPdSvBB5W1Z9Zx1cD70vum3H8WURfEra55Y1WuHEilY0C3yJ6Kf4ucDfwT6q6xQq/Oj6fdBDuBb6r0VqSWXnbF/j7CnnbnWiFHTtvv0y6KWlR3l5E9GLNyluPqA6aeTtXVR/PyVvV+5aat5Fh0F3ztjYWDyRdB6yMf68n0nmdGO9fnRK2R6TnewLYLT4+zcLBvauIVBpHEqlHjgTuj3+/zIrzatewtkxEOjVTl2cP4G0wZbLOXZMixxjRA/UlIhXLOcA7iXpCSbgyVi1lwl5nnF8OXBT/fqp9H5biBuzVULzrmggbturbSHngGfav9nYdsJcVfExVnwRQ1TuJGsPXSrSYqr3MyqyqzqnqVuDnGn8+q+o2IjOyhMOIVAF/AWzSqFe3TVV/oqo/seL81RJhAcZiO+F1RL3Lh2MZthB9SppcLyLvjn//TEQOi8vnYKKBFBNV1b6qnqeqxxPp5z9PpIa43Up/kmgwcDmwOj6+DFhgZ1wyLOxyPloGrIyFujstrIisjm2TbxKRX4jIoyKyIT62e0rcqYjID6190976OOvc53PCZtpmx/t7i8gXROSfRGSdiHw8rpNnisg+VljbPnwtkc31GllsH360VSZfiuP9uojsZYU1bbl/NbblviTNllvS7b6zwl4lIn8pIk9fVMAWcVwXisi/icgBInK+iDwuIpeLyPOtsCtF5K9E5AYR2SQiD4vIJSLyrqJ0hppBvw18bkS9sEOJTOTMbT2RB58Z9sfAodaxceCrwJx1/FJgefzbHNBYTcqAArssGf4Rq0deNSxwJ1HjeEf8f5/4+EoW93ZXA6cSqR4uJWqAbwd+QqSmMMNenZPmcuN3GauWMmFPBK6Nz98EvDs+vidwcYpM5xLpG/c2ju0dHzvPCvuCjO1XgfutsE721hXCnkOkJz0pzudHiHTR7ydSVZhhy9iHm2aHXwT+mqiufwj4dytsGZPPMmHvAD5NpMK4LE5734y6dBmRqu84Ir31W+LjRwE/tcJ+l8iiZ3/gT4D/SWSJcxrRmMfA25omtoEL4DUz0Wf2r2ec+7q1v7/5QFvnXmLtL8sItweGLW/K+de7Vp4yYa3rlmNZMxjndgOeFzc+qZ+7wMEl0nKyaqkQ9tnx+UMcZLjZ9RzRYOCP40bF3rZZYa+x9lPtrSuEvdr4bavK7HjK2IdflROPvV/GRr1MWFOGlxJ9UT0Ql+8JVti8crja2retKS6P/4+RYmY6KtvABQhb2MpsRKaLf26+XIhUUB8BfmSFvR44KCOee6x9J3vrCmF/Zvz+a+tcHdv3e4l6jR8m+goxPeEq23KXDJv2VdgjUnF9xTr+U6Jxid8m+mJ6U3z8ZSzucf8XcaeKaED1XONc5st42LeBCxC2sJXZiDwxP0mk0vhFvG2Ij62xwr4FeGZGPG+y9p3srSuE/SvigWLr+DOAb+Xks8g+/GPWlgzo7g18NSX8kaTbqKfZHzuFJTJNc71vzyNSMf0QOCRu5B8neoH9mhX2uURqjceA/yT+eiNSXX1g0HWwsbo9aAHCFjZfG7G+eVTCElnrPGeQMgxz2GHbloydcWD0EZG7VfWpIWwIO4x0aUHSQKAQEbk26xSW+WIIO/phR4nQGAeGjb2A1xDpE02EaOAnhF1aYUeG0BgHho3vEw2IXWOfEJGLQtglF3ZkCDrjQCAQ6AAj5Q4dCAQCw0pojAOBQKADhMY4EAgEOkBojAOBQKAD/P8FgriZo41GvgAAAABJRU5ErkJggg==",
      "text/plain": [
       "<Figure size 432x288 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "sns.heatmap(X2)\n",
    "plt.title('X2')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(0.5, 1.0, 'X3')"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "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",
      "text/plain": [
       "<Figure size 432x288 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "sns.heatmap(X1 + np.linalg.matrix_power(X1, 2) + np.linalg.matrix_power(X1, 3))\n",
    "plt.title('X3')"
   ]
  }
 ],
 "metadata": {
  "interpreter": {
   "hash": "2497819141e8ba68491e095adc461a03e742be7ecd39014decbc2aa0e30dc29f"
  },
  "kernelspec": {
   "display_name": "Python 3.9.10 64-bit (windows store)",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.9.10"
  },
  "orig_nbformat": 4
 },
 "nbformat": 4,
 "nbformat_minor": 2
}
